Answer:
10
Step-by-step explanation:
10-7 do it yourself and don't vheat
n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. What is the probability that at least 22 of the 44 students selected are non-history majors
Answer:
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Step-by-step explanation:
The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Approximation:
We have to use the mean and the standard deviation of the hypergeometric distribution, that is:
[tex]\mu = \frac{nk}{N}[/tex]
[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]
In this question:
88 + 88 = 176 students, which means that [tex]N = 176[/tex]
88 non-history majors, which means that [tex]k = 88[/tex]
44 students are selected, which means that [tex]n = 44[/tex]
Mean and standard deviation:
[tex]\mu = \frac{44*88}{176} = 22[/tex]
[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]
What is the probability that at least 22 of the 44 students selected are non-history majors?
Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 22}{2.88}[/tex]
[tex]Z = -0.17[/tex]
[tex]Z = -0.17[/tex] has a p-value of 0.4325
1 - 0.4325 = 0.5675
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
I need help answering this ASAP
Answer:
A
Step-by-step explanation:
The graph is a square root function
what is the main protein of a scientific investigation A. To form an opinion B. to test a hypothesis C. To persuade a bias D. To teach a lesson
Answer:
D.To teach a lesson
Step-by-step explanation:
Hope it helps you
HELP PLEASE!
The length of a rectangle is 2V5. The width of the same rectangle is 5V5. Find the perimeter and area of the rectangle.
Answers:
[tex]\text{Perimeter} = 14\sqrt{5}\\\\\text{Area} = 50\\\\[/tex]
=======================================================
Work Shown:
[tex]L = 2\sqrt{5} = \text{length}[/tex]
[tex]W = 5\sqrt{5} = \text{width}[/tex]
P = perimeter
[tex]P = 2*(L+W)\\\\P = 2*(2\sqrt{5}+5\sqrt{5})\\\\P = 2*(7\sqrt{5})\\\\P = 14\sqrt{5}\\\\[/tex]
-------------
A = area
[tex]A = L*W\\\\A = (2\sqrt{5})*(5\sqrt{5})\\\\A = (2*5)(\sqrt{5}*\sqrt{5})\\\\A = 10\sqrt{5*5}\\\\A = 10\sqrt{25}\\\\A = 10*5\\\\A = 50\\\\[/tex]
PLEASE HELP FAST!! WILL GIVE FIRST PERSON THAT RESPONDS A HIGH RATING AND POINTS!
Answer:
Step-by-step explanation:
3
In how many ways can a committee of 3 men and 2 women can be formed from 7 men and 5 women?
Answer:
in five (5) ways a committee can be formed from 7 men and 5 women
Find the total surface area of the square pyramid in the figure.
Question 8 options:
A)
64 yd.^2
B)
224 yd.^2
C)
112 yd.^2
D)
144 yd.^2
Answer:
D
Step-by-step explanation:
Surface area is area of base plus all 4 sides. Base is a square with s = 8 so area is 64sq yd. Sides are triangles, with A = 1/2 bh, so 1/2(8)(5) = 20. Four sides would be 80sq yds. Add base and sum is 144 sq yds.
Anna earned $9 an hour babysitting. She wants
to buy a 16 GB iPod that is $120. Anna has
saved $45 so far. How many more hours of
babysitting does she need to do to earn the rest
to purchase the iPod
Answer:
8.33 hours
Step-by-step explanation:
120-45 = 75
75 ÷ 9 = 8.33
what is the volume of a rectangular prism with length 5cm, width 3cm and height 4cm?
Answer:
60 cm^3
Step-by-step explanation:
The equation to find the volume for a rectangular prism is length times width time height.
So just multiply 5 times 3 times 4
V=(5)(3)(4)
V=60
Answer:
60cm^3
Step-by-step explanation:
w=3cm
h=4cm
l=5cm
[V=whl]
V=3×4×5=60
Three brothers enter a race with 8 friends. The racers draw lots to determine their
starting positions. What is the probability that the older brother, Mike, will start in lane 1, with
his other brothers, Stan and Steve beside him in lanes 2 and 3 in that order?
This figure shows △ABC. BD¯¯¯¯¯ is the angle bisector of ∠ABC.
What is AD?
Answer:
AD = 8/3 units
Step-by-step explanation:
Based on the angle bisector theorem, angle bisector BD divides AC into AD and CD such that they are proportional to AB and CB.
This implies:
AB/AD = CB/CD
AB = 8
CB = 10
Set AD equal to x
AD = x
CD = 6 - x
Substitute the values
8/x = 10/(6 - x)
8(6 - x) = 10(x)
48 - 8x = 10x
48 - 8x + 8x = 10x + 8x
48 = 18x
48/18 = 18x/18
8/3 = x
x = 8/3
AD = 8/3 units
Answer:8/3
Step-by-step explanation:
I just took the quiz
f(x) = 3x3
3.3 – 2.02 + 4x - 5
g(x) = 6x - 7
Find (f + g)(x).
Answer:
C) (f+g)(x)= 3x^3-2x^2+10x-12
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
The number is 6.
Step-by-step explanation:
[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]
What are the factors of 60 ???
Answer:
Factors are 1,2,3,4,5,6,10,12,15,20,30,60
Step-by-step explanation:
Hope this helps
Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.
thus these numbers are factors of 60.
Write this ratio as a fraction in simplest form without any units.
7 gallons to 40 quarts
9514 1404 393
Answer:
7/10
Step-by-step explanation:
In order to make the units cancel, they must be the same. There are 4 quarts in 1 gallon, so 40 quarts = 10×4 quarts = 10×(1 gal) = 10 gal.
Then the ratio is ...
(7 gal)/(10 gal) = 7/10
Rewrite the expression as the algebraic expression in x
Sin
(tan^-1(x))
9514 1404 393
Answer:
sin(tan^-1(x)) = x/√(x² +1)
Step-by-step explanation:
We know that for an angle in a right triangle...
Tan = Opposite/Adjacent
and
Sin = Opposite/Hypotenuse
so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...
Hypotenuse² = Opposite² + Adjacent² = x² +1
Then the sine of the angle is ...
sin(tan^-1(x)) = x/√(x² +1)
find the LCM of 210, 280, 360 by prime factorisation
Answer:
Step-by-step explanation:
210=2x3x5x7
280=2x2x2x5x7
360=2x2x2x3x3x5
Answer:
210= 2×3×5×7
280=2×2×2×5×7
360=2×2×2×3×3×5
common factors=2×2×2×3×5×7=840
uncommon factors=3
L.C.M=Common factors× uncommon factors
L.C.M=840×3
L.C.M=2520
Step-by-step explanation:
i hope it will be helpful
plzz mark as brainliest
The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18 inches and a second side that is 3 inches less than twice the third side, what are the possible lengths for the second and third sides?
Answer: One side could be 18 and the other side will be 33.
Step-by-step explanation:
Side #1 = 18Side #2 = 2x - 3Side #3 = xOne way of setting up the inequality is: Side #2 + Side #3 > Side #1
[tex]2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7[/tex]
Another way of setting up the inequality is: Side #1 + Side #3 > Side #2
[tex]18+x>2x-3\\18+3>2x-x\\x<21[/tex]
Final way of setting up the inequality is: Side #1 + Side #2 > Side #3
[tex]18+2x-3>x\\15>x-2x\\15>-x\\x>-15[/tex]
Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.
The number formed by subtracted 1 from smallest 7-digit number is
Step-by-step explanation:
the number formed by subtracting 1 from the smallest 7 digit number is largest 6 digit number.
What is the slope-intercept equation of the line below?
10 minutes left
Answer:
y=-3x+4
Step-by-step explanation:
The y intercept is 4 because the line crosses the y axis at the 4 tic mark
The slope will be -3 because the y decreases by 3 every time the x incerases by 1
y=mx+b
y=-3x+4
what is Collatz conjecture?
Is Collatz conjecture always true?
What so special about 3x+1 ?
Answer:
Step-by-step explanation:
The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.
Simply put it says
if a number is even, divide by 2If a number is odd, multiply by 3 and add1. or 3x + 1The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.Try 5
It's odd so triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2. You get 22 is even. Divide by 2. You get 11 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.
Take 15It's odd. Triple it and add 1. That gives 46.46 is even. Divide by 223 which is odd. Triple it and add 1 = 7070 is even. Divide by 2. 3535 is odd. Triple and add 1. 106 which is even53 which is odd. Triple it and add 1. You get 160160 is even. Divide by 2. You get 8080 is even Divide by 2. You get 4040 is even. Divide by 2. You get 2020 is even. Divide by 2. You get 1010 is even. Divide by 2. You get 55 is odd. Triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2.. You get 2.2 is even. Divide by 2. You get 11 is odd and you are in the loop because you get 4 which you have already done.Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answer:
y=8 and x=8 ✔3. the check is meant to be square root symbol lol
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
HELP
Answer:
8 cm^2
Step-by-step explanation:
If the triangle is isosceles the sides are the same
Let the sides be x
We know that we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse
x^2+x^2 = (4 sqrt(2))^2
2x^2 =16(2)
2x^2 = 32
Divide by 2
2x^2/ 32/2
x^2 = 16
Taking the square root of each side
sqrt(x^2) = sqrt(16)
x = 4
The area of the triangle is
A =1/2 bh
A = 1/2 (4) (4)
A = 1/2(16)
A = 8
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
c = [tex]4\sqrt{2}[/tex]
[tex]c^{2} = 32[/tex]
a^2 + b^2 = 32
a=b (isosceles triangle)
a=b=4
base = 4
height = 4
area = 1/2 bh = 1/2(4)(4) = 8
If the triangle above is translated two units to the right, what is the correct coordinate for A'?
Answer: 0, 5
Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5
Which expression is equivalent to:
15x + 20y
5(4x+3y)
5(3x+4y)
5y(3x + 4)
Answer:
5(3x+4y)
Step-by-step explanation:
True or false? If it is false, replace the underlined word with the correct word. (Constant is underlined) The constant term in a polynomial expression is a number that is not multiplied by a
variable.
Answer:
true
Step-by-step explanation:
what else would it be. that is exactly the reason why we have constants.
Solve |6k + 12| + 9 = 9 for k.
Step-by-step explanation:
6k + 12 + 9=9
6k + 12 = 9 - 9
6k + 12 = 0
12 = -6k
12/-6 = -6k/-6
2/-1 = k
k = -2
Answer:
k=-2
Step-by-step explanation:
6k+12+9=9
subtract 9 from both sides
6k+12=0
subtract 12 from not sides
6k= -12
divide both sides by 6 (isolating the variable)
k= -12/6
simplify
k= -2
Gabrielle's age is two times Mikhail's age. The sum of their ages is 30 . What is Mikhail's age?
Step-by-step explanation:
G=2m
m+G=30
m +2m =30
3m=30
m=10
Which graph best represents the equation -4x + 5y = 8
Answer:
a or b
Step-by-step explanation:
the pictures are a little hard to tell apart but im my opinion go for a because its the closest
Answer:
A.)
Step-by-step explanation:
I took the test.
Bob travels from Inglewood to anytown; a distance of 20 km.
He walks 800 meters and cycles the rest of the way.
What percentage of the journey does he travel by bicycle?
Answer:
Total Distance = 20km = 20 × 1000 = 20,000 m
Distance walked = 800m
Distance travelled by cycle = 20,000 - 800 = 19,200m
Percentage of journey by cycle = (distance travelled by cycle ÷ total distance) × 100
Percentage of journey by cycle = (19200 / 20000) * 100
Percentage of journey by cycle = 96%
